Corrections to Classical Matrix Ensemble Moments, Non-Crossing Annular Pairings, and Ribbon Graphs

We elucidate a bijection between ribbon graphs on the real projective plane and non-crossing annular pairings that relate to the $1\mathrm{/}N$ correction term of the GOE and LOE spectral moments. We also derive analogous objects for the $1\mathrm{/}{N}^2$ correction terms of said moments and their equivalents for the GUE and LUE.